Hard energy gap in the insulating regime of nominally granular films near the superconductor-insulator transition

A hard gap has been found on the insulating side of the thickness-tuned superconductor-insulator (SI) transition of sequences of nominally granular quench-deposited films of several different metals. This gap increases with decreasing conductivity and increasing disorder. The behavior of the activation energy with high-temperature conductance is surprisingly consistent with a theory of the SI transition in three dimensions that analyzes the competition between Anderson localization and superconductivity and takes into account the fractal nature of the localized single-particle excitations near the mobility edge. This hard gap is similar to the parity gap of a system of small grains but with the localization length replacing the grain size. Similar behavior is not found in the insulating regime close to critical resistance of the SI transition of nominally homogeneous quench-condensed films. This may result from the larger localization length in the latter, resulting in closer and unobservable spacings of the energy levels of the localized quasiparticles.